Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!shadooby!samsung!usc!ucsd!ucbvax!hplabs!hpl-opus!hpnmdla!hpsad!cj
From: cj@hpsad.HP.COM (Chris Johnson)
Newsgroups: comp.graphics
Subject: Re: Excluding Mandelbrot set
Message-ID: <480003@hpsad.HP.COM>
Date: 22 Nov 89 01:37:28 GMT
References: <3544@quanta.eng.ohio-state.edu>
Organization: HP Signal Analysis Division - Rohnert Park, CA
Lines: 22

> The basic idea is to avoid running through the "maximum" number of iterations
> for each point in the Mandelbrot set.  Is this possible, or alternately, is
> there a more acceptable algorithm in terms of speed?
> 
> 							Much obliged,
> 							    Mike

Unfortunately, the definition of the mandelbrot set is:

	     2
	Z = Z  + C

where Z & C are complex, and successive iterations with Z starting at
(0 + 0i), Z does not ever atain a magnitude greater that 2. This implies
that one must, necessarily, go through some number of iterations to determine
whether or not the magnitude of Z is going to "blow up" or stabilize. Actually,
I'm not sure about the limit of 2, maybe it's just whether or not it blows up.
If anyone knows of any other way to do this, please send it in, also please
feel free to correct me if I am wrong, I don't claim to be a mathmatician...

-cj
cj@hpsad.hp.com